This invention relates to a superconducting electromagnet for use is a nuclear magnetic resonance (NMR) imaging apparatus, and more particularly to a superconducting electromagnet which can create a magnetic field of high linearity.
FIG. 1 is a longitudinal cross-sectional view of the superconducting electromagnet of a conventional NMR imaging apparatus of the type to which the present invention relates. As shown in this FIGURE, a superconducting coil 1 for generating a high-uniformity static magnetic field is housed within an inner vessel 2 which maintains the coil 1 at a cryogenic temperature. The inner vessel 2 is surrounded and insulated by a vacuum vessel 3. A heat shield 4 for decreasing the penetration of heat into the inner vessel 2 is disposed between the inner vessel 2 and the vacuum vessel 3. It is maintained at a temperature between that of the inner vessel 2 and that of the vacuum vessel 3. The heat shield 4 is made of a material having good thermal conductivity such as copper or aluminum. The inner periphery of the vacuum vessel 3 surrounds a tubular frame 6 which is parallel to the longitudinal axis (the z axis) of the apparatus. Z gradient coils 5 which generate a magnetic field which linearly varies in strength along the z axis in the region in which imaging is performed are wound around the tubular frame 6.
FIG. 2 schematically illustrates the structure of the z gradient coils 5. They can be modelled as a pair of annular coils 5a and 5b of radius a.sub.c having a current I.sub.c flowing through them in opposite directions. In the coordinate system of FIG. 2, the coils 5a and 5b are coaxial with respect to the z axis and the z coordinates of their centers are respectively +z.sub.c and -z.sub.c.
The magnetic field B(z) which is formed by the coil system of FIG. 2 at an arbitrary point on the z axis is given by the equation EQU B(z)=(.mu..sub.o I.sub.c /a.sub.c).multidot.{.epsilon..sub.1 (.beta.).multidot.(z/a.sub.c)+.epsilon..sub.3 (.beta.).multidot.(z/a.sub.c).sup.3 +.epsilon..sub.5 (.beta.).multidot.(z/a.sub.c).sup.5 + . . . } (1)
wherein .mu..sub.o is the permeability of empty space, and .epsilon..sub.1 (.beta.), .epsilon..sub.3 (.beta.), and .epsilon..sub.5 (.beta.) are functions of .beta.=z.sub.c /a.sub.c. When performing NMR imaging, it is desirable that the magnetic field B(z) be as nearly linearly proportional to z as possible near the origin. Such a linearly-varying magnetic field can be obtained by adjusting the positions of the z gradient coils 5a and 5b so that the cubic term and all higher-order terms in Equation (1) vanish. The value of the function .epsilon..sub.3 (.beta.) is given by the following equation: ##EQU1##
Therefore, if .beta. is chosen to be .+-..sqroot.3/2, then .epsilon..sub.3 (.beta.)=0, and the cubic term in Equation (1) will disappear. Furthermore, in the region in which .vertline.z.vertline.&lt;a, all the terms of Equation (1) of 5th order and above are small compared to the linear term and can be ignored. Accordingly, if .beta. is set equal to .+-..sqroot.3/2, a magnetic field can be generated which is nearly linearly proportional to the z coordinate in the vicinity of the origin.
However, the above analysis assumes ideal conditions in which only the z gradient coils 5 contribute to the magnetic field. In actual operation, the current passing through the z gradient coils generates eddy currents in the heat shield 4. These eddy currents generate a nonlinearly varying magnetic field, and when this magnetic field is added to the magnetic field expressed by Equation (1), the resulting composite magnetic field does not linearly vary along the z axis.
In order to prevent eddy currents from being induced in the heat shield 4, in some superconducting electromagnets for NMR imaging, the heat shield 4 is divided into a plurality of parallel strip-shaped conductors 4a separated by gaps, as shown in FIG. 3. However, because of the difficulty of electrically insulating the strip conductors 4a from one another and at the same time physically connecting them so as to form a single body, the structure of such a heat shield 4 is complicated and therefore the heat shield 4 is expensive to manufacture.